The dimensions of a rectangle can be expressed as x+4 and x-3. If the area of the rectangle is 60 inches squared, find the dimensions of the rectangle

Answer:

Step-by-step explanation:

Find x:-

[tex]\sf 11x-9+72+6x-2=180[/tex]

[tex]\sf 17x+61=180[/tex]

[tex]\sf 17x=119[/tex]

[tex]\sf x=7[/tex]

Find y:-

[tex]\sf 30+11(7)-9+5y-8=180[/tex]

[tex]\sf 5y+90=180[/tex]

[tex]\sf 5y=90[/tex]

[tex]\sf y=18[/tex]

So, therefore, x = 7° & y = 18°!!

____________________

Hope this helps!

Have a great day! :)

The factor of the expression 27 + 33 is 3.

What is meaning of factor?

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Factors can be found using either division or multiplication. Rules of divisibility can also be applied.

What meaning of expression?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Given expression is 27 + 33

The factors of 27 are 1, 3, 9, 27.

The factors of 33 are 1, 3, 11, 33.

The common factor of 27 and 33 is 3.

Taking common 3 from the given expression:

27 + 33 = 3 (9 + 11)

The factor of the given expression is 3.

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The p-value is higher than 0.05, so we are unable to rule out the null hypothesis. There is little proof to back up the director's claim.

Hypothesis:

H₀ : μ = 3000

H₁ : μ > 3000

The t-test should be employed when the population mean and standard deviation are unknown. Since the sample size is high, we can infer that the sample mean's sampling distribution is normal.

The following information is provided:

s = 450

x = 3200

n = 14

Therefore, test statistics will be:

t = (x - μ) / (s / √n) = (3200 - 3000) / (250 / √14) = 1.66

The test in this instance is right-tailed, and its degree of freedom is df=n-1=14-1=13.

0.0601 is the p-value.

We are unable to reject the null hypothesis since the p-value is higher than 0.05. The director's allegation is not supported by a lot of evidence.

Since p =.0601, the director's assertion cannot be supported by the available data.

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Answer:

X = 14

Hope this helps!

Step-by-step explanation:

The small red square means the angle is 90°.

( 2x + 22 ) + ( 3x - 2 ) = 90°

2x + 22 + 3x - 2 = 90

( 2x + 3x ) + ( 22 - 2 ) = 90

5x + 20 = 90

5x + 20 - 20 = 90 - 20

5x = 70

x = 14

Answer: x = 14

Step-by-step explanation:

When you have a right angle, they add up to 90 degrees

So you add up the two angles that you have that equal a total of 90 degrees

2x+22 + 3x-2 = 90

5x+20 = 90

5x = 70

x = 14

I hope this helps :D

P(x) is a polynomial function having rational coefficients that has given roots is: P(x) = x³ + 2x² + 4x + 8.

P(x) has given roots: -4 and 2i. ​

A radical is always preceded by a pair of plus & minus signs.

As a result, there would be another root -2i.

All of the roots are -4, -2i, + 2i.

As, the number of roots given are 3, thus the polynomial formed ill be cubic.

The roots in terms of the polynomial can be written as-

P(x) = (x - (-2))(x - 2i)(x + 2i)

P(x) = (x + 2)(x - 2i)(x + 2i)

Simplifying,

P(x) = x³ + 2x² + 4x + 8

Thus, P(x) is a polynomial function having rational coefficients that has given roots is P(x) = x³ + 2x² + 4x + 8.

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A graph of the given equation (x - y = 6) is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.

Next, we would rewrite the given equation in standard form as follows:

x - y = 6

Adding y to both sides of the equation, we have the following:

x - y + y = 6 + y

x = 6 + y

Rearranging the equation, we have the following:

y = x - 6

By critically observing the graph (see attachment), the y-intercept is equal to -6 and the x-intercept is equal to 6.

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The equivalent expressions are 7y + 2y+y and 10y & 8m-4m+4m and 8m.

Other expressions are not equivalent

Expressions 1

The expressions are given as

4(2a+7) and 8a +7

Open the brackets

8a+28 and 8a +7

The above expressions are not equal

Expressions 2

Here, we have

7y + 2y+y and 10y

Evaluate the like terms

10y and 10y

The above expressions are equal

Expressions 3

Here, we have

8m-4m+4m and 8m

Evaluate the like terms

8m and 8m

The above expressions are equal

Expressions 4

Here, we have

9e+2(e+5) and 11 +5

Open the brackets

9e+2e+10 and 11 +5

Evaluate the like terms

11e + 10 and 11 + 5

The above expressions are not equal

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Answer:

5.090 x 10^-5

Step-by-step explanation:

Exceed relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample.

An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values. A sample is that precise value. The probability distribution of the random variable determines the possible values and the likelihood of each. Using samples, one can draw conclusions about populations. Since samples are useful, affordable, practical, and manageable, it is simpler to gather data from them. A crucial component of the scientific method is sampling, which enables researchers to demonstrate the validity of generalizable ideas using only a sample of particular facts. Additionally, sampling enables mathematicians to answer challenging paradoxes like the St.

Given,

Exceed relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The function shown in the graph above is a discontinuous function, at x = -2

For values of x less than -2, the left side of the graph is applicable. whose equation is :

[tex]\qquad \sf  \dashrightarrow \: y - 0 = \cfrac{1 - 0}{ - 3 - ( - 2)} (x - ( - 2))[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \cfrac{1}{ - 3 + 2} (x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - 1(x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - x - 2 \:\: ; \:\:x<-2[/tex]

For values of x greater than -2, the right side of the graph is applicable. whose equation is :

[tex]\qquad \sf  \dashrightarrow \: y - 4= \cfrac{4 - 2 }{0 - (-2)} (x -0)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 4 = \cfrac{2}{2} (x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 4 = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = x + 4 \: \: ;\: \: x > - 2[/tex]

So, the correct choice will be Option " A "

Answer:

[tex]\textsf{A.} \quad \begin{cases}-x -2 \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]

Step-by-step explanation:

When graphing piece-wise functions:

From inspection of the given graph:

Therefore, the definition of the function is:

[tex]\begin{cases}-x + a \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]

where a is some constant.

The only answer option that matches the given parameters is option A.

The height of the poster is 20 inches.

The original width of the poster was 6 inches. The original height of the poster was 4 inches. The size of the poster is scaled up. This is a transformation of the size of the poster. The width of the scaled-up poster is 30 inches. We need to find out the height of the scaled-up poster.

The scaling transformation preserves the shape of the object. This means the sides must still be in the same proportion. Let the constant of proportionality be represented by the variable "k".

30 = k*6

k = 30/6

k = 5

Hence, the poster is scaled up by a factor of five.

H = k*4

H = 5*4

H = 20

Hence, the height of the scaled-up poster is 20 inches.

The complete question is given below.

Amir wants to scale up a photo to create a poster for his room. The original picture is 6 inches in width and 4 inches in height. What will be the height of the poster if its width is 30 inches?

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ANSWER: 137

Step-by-step explanation:

This can be rewritten as:

18 × 7 - (-1)² -(-9)

Using BODMAS

firstly open the brackets using the negative sign, we have;

18 × 7 +1² + 9

Now you can apply your BODMAS.

126 + 1 + 9

ANS = 137

The probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

In the given probability case we have;

What is the likelihood that, out of a random sample of 500 persons, fewer than 60 will work from home if 15% of adults in a particular country do so?

Let,

P = 15% = 0.15

n = 500

By considering the binomial distribution case the formula is given by

P( X = x ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

P( X ≤ 60 ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

                 = ⁶⁰∑ₓ=₀ (⁵⁰⁰Cₓ) (0.15)ˣ (1 - 0.15)⁵⁰⁰⁻ˣ

                 = 0.031

                 ≅ 0.03

Hence, the probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

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Last year, Maria earned $54,000

In this question, we have been given  Maria earns a $50,000 salary plus a 10% commission on any sales over $20,000.

Last year Maria made $40,000 in sales.

This means, she got 10% commission

We find the 10 percent of 40000.

40000 * (10/100) = 4000

Her total earning would be,

$50,000 + $4000(commission) = $54,000

Therefore, Maria earned $54,000

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The volume of the composite solid is 340.4 cubic inches

The composite solid is made up of two parts one has

The volume for the uniform height  

= base area * height

base area = 0.5 base * height = 0.5 * 8 * 6.9 = 27.6

= 27.6 * 10

= 276 cubic inches

The volume for the varying height

= 1/3 base area * height

base area = 27.6 (both share same base)

= 1/3 * 27.6 * 7

= 64.4 cubic inches

The total volume

= 276 + 64.4

= 340.4 cubic inches

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Using the concept of application of derivative it is concluded that the rate of change in the area of square tile is 94.25 cm²/hour.

The area of the square is defined as the square of its sides.

Let the side of the square is a then its area will be a².

Area of square figure = Side².

Let the side of the square is x= 29cm.

It is given that the side 29 cm tile is growing by 1.625 cm per hour on heating.

And the rate of change in side of square dx/dt = 1.625 cm/hour

We have to calculate the rate of change in an area of the square (A).

hen, area A = x²

On differentiating A with respect to time(t) we get a rate of change in area

dA/dt = d(x²)/dt

= 2x dx/dt

= 2×29×1.625

= 94.25 cm²/hour

Hence, the rate of change in the area of the square tile is 94.25 cm²/hour.

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Answer:

y = 1x + -2

Step-by-step explanation:

Step 1: Calculating Slope (m).

m = y2 - y1 / x2 - x1

m =  -4 - 0 / -2 - 2

m = -4 / -4

m = 1

Now put value of m in equation...

y = 1x + b

Step 2: Calculating Y-intercept (b).

Lets choose the first point, ( 2, 0) for calculating y-intercept:

y = m ( x ) + b

0 = 1 ( 2 ) + b

0 = 2 + b

-2 = b

b = -2

Now put value of b in equation for your final answer...

y = 1x + -2

Hope this helps!

Slope:

The slope is found with m = (y2 - y1) / (x2 - x1).

You can use any two points, so I'd pick ones with positive x and y values.

Using (1,5) and (3,3):

    m = (3 - 5) / (3 - 1) = (-2)/(2) = -1

The slope is -1.

To find the y-intercept, we can go to the point (-1,7) and use the slope of -1.  A slope of -1 means that if x goes up by 1, then then y goes down by 1.  So if we go from x=-1 to x=0, then the y-value of 7 will go down by 1.

y-intercept (0,6)

The equation in slope-intercept form is y = -x + 6, since we already found the slope and y-intercept.

The speed of the faster car is 40 miles/hr.

both cars travel for same time , so let that time be 't'

car 1 :

distance travelled = 75 miles

let the speed of the car be = x miles/hr

∴ time (t)  = distance / speed

              t  =   75 / x               .............(1)

car 2 :

distance travelled = 100 miles

speed of the car is = x + 10 miles/hr  ( already provided )

∴  time ( t) = distance / speed

            t  = 100/ (x+10)        ..............(2)

    now as the time for both the cases is same  , so we equate eqn (1) and eqn (2) .

∴ 75/x  =  100/ (x+10)

3x + 30 = 4x

x = 30

so the speed of the 1st car will be 30 miles / hr

and the speed of the 2nd car ( faster car ) will  be x + 10 = 40 miles/hr

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Answer:

6

Step-by-step explanation:

3x-7=11

3x-7=113x=11+7

3x-7=113x=11+73x=18

3x-7=113x=11+73x=183x/3=18/3

3x-7=113x=11+73x=183x/3=18/3 X=6

The locations of the destinations given by the angles formed between parallel lines and their common transversal in the question are;

1) US Capitol

2) CIA Building

3) US Capitol

4) US Treasury

5) Walmart

The relationship between the angles formed are;

1) The location that is at a corresponding angle to the White House is the Supreme Court

The location at the vertical angle to the Supreme Court is the Smithsonian Institute

The location that is at the angle right adjacent to the Smithsonian Institute is the US Capitol

2) The location that is vertical angles to the FBI Building is the National Zoo

The same side interior angle to the National Zoo is the National Coffee shop

The location at the alternate interior angle to the National Coffee Shop is the CIA Building

3) The location at the alternate exterior angles to Lincoln Memorial is Walmart

The adjacent location that is a right angle to Walmart is the White House Gardens

The location that is at the corresponding angle to the White House Gardens is the US Capitol

4) The location that is at the corresponding angle location to the Smithsonian Institute is the National Zoo Gift Shop

The location that is at the same side interior angle to the national gift shop is the US Capitol

The location that is at the vertical angle location to the US Capitol is the US Treasury

5) The location that is at alternate interior angle location to the Ford's theater is the US Capitol.

The location that is supplementary with the Vietnam War Memorial and the National Zoo is the National Coffee Shop

The location at the angle that is vertical from the National Coffee Shop is the Lincoln  Memorial

The location that is at alternate exterior angle with the Lincoln Memorial is Walmart

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Answer: 67

Step-by-step explanation:

do the math

The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is: [tex]y = \frac{5}{8} x + \frac{1}{8}[/tex]

Calculation

from ( - 3, 2) and (5, 7)

slope(m)  = [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]

[tex]=\frac{7 - 2}{5 - (-3)}[/tex]

[tex]= \frac{5}{8}[/tex]

from slope-intercept equation

⇒y = mx+ c

⇒( - 3, 2) , [tex]2 = \frac{5}{8} * (-3) + b[/tex]

⇒[tex]2 = \frac{15}{8} + b[/tex]

⇒[tex]2 - \frac{15}{8} = b[/tex]

⇒[tex]\frac{16+15}{8} = b[/tex]

⇒[tex]\frac{31}{8} = b[/tex]

Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :

⇒[tex]y = \frac{5}{8} x +\frac{31}{8}[/tex]

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The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is:

One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line.

When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).

The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,

Slope-intercept form

Point slope form

Two-point form

Intercept form

from ( - 3, 2) and (5, 7)

slope(m)  = y²-[tex]y^{1}[/tex]/x²-[tex]x^{1}[/tex]

=7-(-2)/5-(-3)

=5/8

from slope-intercept equation

⇒y = mx+ c

⇒( - 3, 2) , 2=5/8*(-3)+b

⇒2=15/8+b

⇒2-15/8=b

⇒16+15/8

31/8=b

Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :

⇒y=5/8x +31/8

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Answer:

2 minutes for a whole song.

Step-by-step explanation:

Given that,

→ (1/6) song = (1/3) minutes

Parts of whole song is,

→ (1/6) × 6 = 1

Then the required minutes taken to play whole song will be,

→ x/6 = 1/3

→ x = (1/3) × 6

→ x = 6/3

→ [ x = 2 min ]

Hence, 2 minutes for a whole song.

Answer:

The coefficient is 7 and the term that has it.

The required probability that there are at least 1 blue candy and 1 green candy left in the jar when you have taken out all the red candies is 7/12 .

Probability is defined as the ratio of total numbers of outcomes of an event to the favouable outcomes of an event.

We have , Red candies in the jar = 10

green canides in the jar = 30

blue candies in the jar = 20

total number of candies in jar = 60 i.e total number of outcomes = 60

The Probability that the last of sixty candies drawn is one of thirty green candies = 30/60 = 1/2

Ignoring green canides, probability that the last of the thirty other candies drawn is one of twenty blue = 20/30 = 2/3

The Probability that the last of sixty candies drawn is one of twenty blue candies = 20/60 = 1/3

The Probability that the last of sixty candies drawn is not one of twenty blue candies = 1 - 1/3

= 2/3

Probability that last draw would be blue and the last not blue would be green = 20/60 × 30/40

= 1/4 ----(1)

Probability that last draw would be green and the last not green would be blue = 30/60× 20/30

= 1/3 ------(2)

Now , Required probability that last draw would be either blue or green canidy = sum of above probabilty from equation (1)and (2)

= 1/4 + 1/3 = 7/12

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A) The matrix equation that represents the given information is;

[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]

B) The cost of a banana is; $0.05

The cost of an orange is; $0.12

A matrix equation is defined as an equation where a variable stands for a matrix .

Let x represent cost of oranges

Let y represent cost of bananas

5 oranges and 14 bananas cost me $1.30 and 8 oranges and 9 bananas

cost me $1.41. Thus, the equations are;

5x + 14y = 1.30  ----(1)

8x + 9y = 1.41   -----(2)

A) Now, the matrix form of the simultaneous equation above will be;

[tex]\left[\begin{array}{ccc}5&14\\8&9\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x&\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.30&\\1.41\\\end{array}\right][/tex]

B) Multiply the first equation by 8 and the second one by 5 to get;

40x + 112y = 10.4

40x +   45y = 7.05   Subtract to get;

            67y = 3.35

Divide both sides by 67 to get;

y = $0.05 per banana

Plug in 0.05 for y into eq 1 to get;

5x + 14(0.05) = 1.30

5x + 0.7 = 1.3

5x = 1.3 - 0.7

5x = 0.6

x = 0.6/5

x = $0.12

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The value of n is -22.

What is a variable?

Any traits, figures, or amounts that may be gauged or counted are considered variables.

Given:

5(n+4)/3=n-8

Move 3 to the right

5(n+4)=3(n-8)

5n+20=3n-24

5n-3n= -24-20

2n=-44

n=- 44/2=-22

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Answer:

57

Step-by-step explanation:

Straight line is 180 degrees

x+2x+9=180

3x=171

x=171/3

x=57

pls mark as brainliest

The complete proof using the AAS congruence postulate and CPCTC is explained below to show that QT ≅  SR.

When two angles of a triangle, and one of its side that is nonincluded are congruent to corresponding two angles and a nonincluded side in the another triangle, then both triangles are congruent by the AAS congruence postulate.

If two triangles are congruent, then all its corresponding parts are also congruent to each other based on the CPCTC theorem.

Below is the two-column proof that proves that side QT is congruent to side SR.

Statement                                     Reasons                                    

1. ∠R ≅ ∠T, QT ≅ SR                    1. Given

2. ∠TQS ≅ ∠RSQ                         2. Alternate interior angles

3. QS ≅ QS                                   3. Reflexive property

4. ΔTQS ≅ ΔRSQ                          4. AAS

5. QT ≅  SR                                   5. CPCTC

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